I understood there would be no fuzzy math

My head hurts from trying to figure this out, and I suspect it is some kind of supply and demand nonsense:

It is cheaper (much) to buy a round-trip airline ticket than one way. The thing is, I need a one way ticket.

So in this day and age of suspecting grandparents of being terrorists for toting a (gasp) camera, what would happen if we bought a round-trip ticket and just, well, never used the second half?

I can get a cheaper one-way ticket if we accept one or two stops, making a two hour flight take all day, and raising the interesting idea of just how the fuck to shove a wheelchair onto one of those tiny airplanes after our layover.